Balance the chemical equation: a extH2 extS + b extSO2 ightarrow c extS + d extH2 extO

For Hydrogen (H):
Reactants: $2a$
Products: $2d$
Equation: $2a = 2d \Rightarrow a = d$

For Sulfur (S):
Reactants: $a$ (from $\text{H}_2\text{S}$) $+ b$ (from $\text{SO}_2$)
Products: $c$ (from S)
Equation: $a + b = c$

For Oxygen (O):
Reactants: $2b$ (from $\text{SO}_2$)
Products: $d$ (from $\text{H}_2\text{O}$)
Equation: $2b = d$

We have:

1. $a = d$
2. $a + b = c$
3. $2b = d$

Substitute equation (3) into equation (1):
$a = 2b$

Now substitute $a = 2b$ into equation (2):
$2b + b = c \Rightarrow c = 3b$

So, we have the relationships:
$a = 2b$
$c = 3b$
$d = 2b$

Let $b = 1$.
Then:
$a = 2(1) = 2$
$c = 3(1) = 3$
$d = 2(1) = 2$

The balanced equation is $2\text{H}_2\text{S} + 1\text{SO}_2 \rightarrow 3\text{S} + 2\text{H}_2\text{O}$.

Reactants:
H: $2 \times 2 = 4$
S: $2 \times 1 + 1 \times 1 = 3$
O: $1 \times 2 = 2$

Products:
H: $2 \times 2 = 4$
S: $3 \times 1 = 3$
O: $2 \times 1 = 2$

All atoms are balanced.

The calculated coefficients are $a=2, b=1, c=3, d=2$. This matches option A.

The final answer is $\text{A. } a=2, b=1, c=3, d=2$.